A dual approach to regularization in image restoration

The restoration of blurred noisy images can be formulated, using the regularization theory, as a constrained optimization problem. According to the classical approach, based on the Lagrange multipliers theory, the exact solution of this problem is obtained iteratively by solving several minimization problems of very large dimensions. This involves enormous computation costs. In this paper, an alternative method, based on the primal-dual theory of convex optimization, is proposed; the original problem is reformulated in an equivalent form so that the related dual problem can be solved through a single unconstrained maximization. The solution of the original problem is then related to the solution of the dual problem via a simple model which depends on the particular cost functional adopted.